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Appearance of stable minimal spheres along the Ricci flow in positive scalar curvature

Antoine Song

Geometry & Topology 23 (2019) 3501–3535
Bibliography
1 S Angenent, Nodal properties of solutions of parabolic equations, Rocky Mountain J. Math. 21 (1991) 585 MR1121527
2 S Angenent, D Knopf, An example of neckpinching for Ricci flow on Sn+1, Math. Res. Lett. 11 (2004) 493 MR2092903
3 S B Angenent, D Knopf, Precise asymptotics of the Ricci flow neckpinch, Comm. Anal. Geom. 15 (2007) 773 MR2395258
4 R H Bamler, Long-time behavior of 3–dimensional Ricci flow : Introduction, Geom. Topol. 22 (2018) 757 MR3748679
5 R H Bamler, Long-time behavior of 3–dimensional Ricci flow, A : Generalizations of Perelman’s long-time estimates, Geom. Topol. 22 (2018) 775 MR3748680
6 R H Bamler, Long-time behavior of 3–dimensional Ricci flow, B : Evolution of the minimal area of simplicial complexes under Ricci flow, Geom. Topol. 22 (2018) 845 MR3748681
7 R H Bamler, Long-time behavior of 3–dimensional Ricci flow, C : 3–manifold topology and combinatorics of simplicial complexes in 3–manifolds, Geom. Topol. 22 (2018) 893 MR3748682
8 R H Bamler, Long-time behavior of 3–dimensional Ricci flow, D : Proof of the main results, Geom. Topol. 22 (2018) 949 MR3748683
9 H D Cao, X P Zhu, A complete proof of the Poincaré and geometrization conjectures — application of the Hamilton–Perelman theory of the Ricci flow, Asian J. Math. 10 (2006) 165 MR2233789
10 B L Chen, X P Zhu, Uniqueness of the Ricci flow on complete noncompact manifolds, J. Differential Geom. 74 (2006) 119 MR2260930
11 O Chodosh, D Ketover, D Maximo, Minimal hypersurfaces with bounded index, Invent. Math. 209 (2017) 617 MR3681392
12 B Chow, The Ricci flow on the 2–sphere, J. Differential Geom. 33 (1991) 325 MR1094458
13 B Chow, D Knopf, The Ricci flow : an introduction, 110, Amer. Math. Soc. (2004) MR2061425
14 B Chow, P Lu, L Ni, Hamilton’s Ricci flow, 77, Amer. Math. Soc. (2006) MR2274812
15 T H Colding, C De Lellis, The min-max construction of minimal surfaces, from: "Surveys in differential geometry" (editor S T Yau), Surv. Differ. Geom. 8, International (2003) 75 MR2039986
16 T H Colding, W P Minicozzi II, Estimates for the extinction time for the Ricci flow on certain 3–manifolds and a question of Perelman, J. Amer. Math. Soc. 18 (2005) 561 MR2138137
17 C De Lellis, D Tasnady, The existence of embedded minimal hypersurfaces, J. Differential Geom. 95 (2013) 355 MR3128988
18 Y Ding, A remark on degenerate singularities in three dimensional Ricci flow, Pacific J. Math. 240 (2009) 289 MR2485466
19 H Federer, W H Fleming, Normal and integral currents, Ann. of Math. 72 (1960) 458 MR123260
20 M A Grayson, Shortening embedded curves, Ann. of Math. 129 (1989) 71 MR979601
21 M Gromov, H B Lawson Jr., The classification of simply connected manifolds of positive scalar curvature, Ann. of Math. 111 (1980) 423 MR577131
22 H L Gu, X P Zhu, The existence of type II singularities for the Ricci flow on Sn+1, Comm. Anal. Geom. 16 (2008) 467 MR2429966
23 R Gulliver, Removability of singular points on surfaces of bounded mean curvature, J. Differential Geometry 11 (1976) 345 MR0431045
24 R S Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982) 255 MR664497
25 R S Hamilton, The Ricci flow on surfaces, from: "Mathematics and general relativity" (editor J A Isenberg), Contemp. Math. 71, Amer. Math. Soc. (1988) 237 MR954419
26 R S Hamilton, The formation of singularities in the Ricci flow, from: "Surveys in differential geometry" (editor S T Yau), Surv. Differ. Geom. 2, International (1995) 7 MR1375255
27 R S Hamilton, Non-singular solutions of the Ricci flow on three-manifolds, Comm. Anal. Geom. 7 (1999) 695 MR1714939
28 T Ivey, Ricci solitons on compact three-manifolds, Differential Geom. Appl. 3 (1993) 301 MR1249376
29 B Kleiner, J Lott, Notes on Perelman’s papers, Geom. Topol. 12 (2008) 2587 MR2460872
30 H Li, X Zhou, Existence of minimal surfaces of arbitrarily large Morse index, Calc. Var. Partial Differential Equations 55 (2016) MR3509038
31 J Lott, N Sesum, Ricci flow on three-dimensional manifolds with symmetry, Comment. Math. Helv. 89 (2014) 1 MR3177907
32 F C Marques, A Neves, Rigidity of min-max minimal spheres in three-manifolds, Duke Math. J. 161 (2012) 2725 MR2993139
33 W Meeks III, L Simon, S T Yau, Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature, Ann. of Math. 116 (1982) 621 MR678484
34 J Morgan, G Tian, Ricci flow and the Poincaré conjecture, 3, Amer. Math. Soc. (2007) MR2334563
35 J Morgan, G Tian, The geometrization conjecture, 5, Amer. Math. Soc. (2014) MR3186136
36 B O’Neill, Semi-Riemannian geometry : with applications to relativity, 103, Academic (1983) MR719023
37 G Perelman, The entropy formula for the Ricci flow and its geometric applications, preprint (2002) arXiv:math/0211159
38 G Perelman, Finite extinction time for the solutions to the Ricci flow on certain three-manifolds, preprint (2003) arXiv:math/0307245
39 G Perelman, Ricci flow with surgery on three-manifolds, preprint (2003) arXiv:math/0303109
40 J T Pitts, Existence and regularity of minimal surfaces on Riemannian manifolds, 27, Princeton Univ. Press (1981) MR626027
41 R Schoen, Estimates for stable minimal surfaces in three-dimensional manifolds, from: "Seminar on minimal submanifolds" (editor E Bombieri), Ann. of Math. Stud. 103, Princeton Univ. Press (1983) 111 MR795231
42 W X Shi, Deforming the metric on complete Riemannian manifolds, J. Differential Geom. 30 (1989) 223 MR1001277
43 L Simon, Lectures on geometric measure theory, 3, Australian National Univ. (1983) MR756417
44 A Song, Embeddedness of least area minimal hypersurfaces, J. Differential Geom. 110 (2018) 345 MR3861813
45 X Zhou, Min-max minimal hypersurface in (Mn+1,g) with Ric > 0 and 2 n 6, J. Differential Geom. 100 (2015) 129 MR3326576